1. Technical Field
This invention relates to antireflective microtextured surfaces. Further, the present invention relates to the optical properties of sub-wavelength gratings. The inventive articles described herein are microstructured antireflective textures designed to reduce diffraction intensity when compared to sub-wavelength gratings already known in the art.
2. Introduction to Prior Art
It is a well known technique to impart antireflective properties to an object, such as a sheet glass, by introducing microscopic corrugations to the surface of the object [see for instance: “Artificial Media Optical Properties-Subwavelength Scale”, Lalanne and Hutley, published in the Encyclopedia of Optical Engineering, 2003]. We refer to such low reflectance surfaces as microstructured antireflective textures (MARTs). The microcorrugations of a MART typically are on a length scale sufficiently small—usually in the sub-wavelength regime—to prevent diffusive scattering of light commonly exhibited by a “matte” or “non-glare” finish. That is, a MART truly reduces the hemispherical reflectance from a surface rather than merely scattering or diffusing the reflected wavefront. In this regime, the interaction of light with a microstructured surface is usually described using an “effective medium theory”, under which the optical properties of the microtextured surface are taken to be a spatial average of the material properties in the region [Raguin and Morris, “Antireflection Structured Surfaces for the Infrared Spectral Region”, Applied Optics Vol. 32 No. 7, 1993). The hemispherical reflectance of light from glass back into air can be less than 0.5% for a properly designed MART. Such a small hemispherical reflectance is impossible if the surface corrugations are much larger than the wavelength of incident light. For visible light, the length scale of MART corrugations is typically around one-half micron.
Perhaps the best known MART is the so-called “moth-eye” surface which possesses optical properties that may be more effective than commercially available thin-film coatings. Thin-film antireflective coatings usually consist of one or more layers of materials optically dissimilar from the substrate, and are sputtered or evaporated onto the substrate in precisely controlled thicknesses. Moth-eye surfaces are comprised of a regular array of microscopic protuberances, and are presently available from a small number of manufacturers worldwide (for example Autotype International Limited, in Oxon, England). Other examples of MARTs are the “SWS surface” [Philippe Lalanne, “Design, fabrication, and characterization of subwavelength periodic structures for semiconductor antireflection coating in the visible domain” pp. 300-309, in SPIE Proceedings Vol. 2776, (1996)], and the “MARAG” surface [Niggemann et al, “Periodic microstructures for large area applications generated by holography” pp 108, Proceedings of the SPIE vol. 4438 (2001)].
Despite moth-eye's excellent antireflective performance, a problem with this particular MART is related to unwanted diffraction. A moth-eye surface designed for the visible waveband exhibits diffraction at oblique angles typically from deep blue to green. When a moth-eye surface is used as an antireflective treatment for a transparent window, this diffraction adulterates the colors of the transmitted image. Therefore, reduction of this diffraction would enhance the value of MARTs as an antireflective treatment for glazing materials for picture frames, TV screens, personal handheld devices, cellular phones, shop windows, and any other application where an image is protected by a window.
Fabrication of the Moth-Eye Microstructure Using Interference Lithography
Clapham and Hutley (U.S. Pat. No. 4,013,465) describe a method to produce a microstructured antireflective texture that is broadband with large angular acceptance of incident light. This MART is characterized by a surface covered with a regular array of conical protuberances, where the feature sizes of the tapered protuberances are in general sub-wavelength. This surface profile was dubbed the “moth-eye” antireflective surface, since Bernhard (Endeavor 16, p. 76-84, 1967) first noticed that the eyes of night flying moths were covered with an array of sub-wavelength protuberances, and hypothesized that the function of this profile was precisely to reduce the reflectivity of the eyes of these moths making them less detectable to predators.
The Clapham and Hutley patent suggests a photo-exposure method to produce the moth-eye microtexture. The patent further discloses the specific technique of “interference lithography” that involves exposing photoresist to an interference pattern from multiple beams of coherent light. A limitation of interference lithography is the strict periodicity of the pattern generated by this technique. If two beams of coherent light are used to expose a sample, a periodic square array of protuberances can be achieved with multiple exposures. If three beams are used, a pattern with hexagonal symmetry is achieved in a single exposure. In general, the details of the exposure can be varied to obtain a pattern with varying degrees of symmetry. Nevertheless the resulting patterns of protuberances will still be periodic with long-range order.
The blue-green diffraction effects observed in typical moth-eye surfaces fabricated by interference lithography is due to the periodicity of the sub-wavelength grating that comprises this MART. To understand this, first consider the diffraction of light from a one-dimensional periodic grating. The typical period or pitch size of a motheye structure designed to work in the visible waveband from 400 nm to 700 nm is d=250 nm. The 1D grating equation is:
                                          m            ⁢                          λ              d                                =                                    (                                                sin                  ⁢                                                                          ⁢                  γ                                -                                  sin                  ⁢                                                                          ⁢                  φ                                            )                        ≤            2                          ,                                  ⁢                  m          =          0                ,                  ±          1                ,                              ±            2                    ⁢                                          ⁢          …                                    (                  EQ          .                                          ⁢          1                )            In this equation m is the diffraction order and φ is the angle of incident light, while γ is the diffracted angle, and the grating has spatial period d. (EQ. 1) is one of the main requirements for constructive interference from a grating with a periodic structure.
Since moth-eye is a sub-wavelength grating, we wish to focus on the case where λ>d for all wavelengths in the band of interest. Since the absolute value of the expression in parentheses of (EQ 1) is no greater than 2, we find that m can only take on the values m={−1, 0, 1}, implying that second or higher order diffraction does not exist for a sub-wavelength grating. Let us consider two important cases, (a) illumination at normal incidence, and (b) illumination at oblique incidence.
Case (a). Incident light is perpendicular to the grating surface, i.e. φ=0. For λ>d the only solution to (EQ. 1) when φ=0 is the zeroth m=0 order. If d=250 nm (smaller than any wavelength in the visible band), we conclude that any visible light normally incident on a sub-wavelength grating does not undergo diffraction into non-zero orders.
Case (b). Light propagates towards the sub-wavelength grating at a grazing angle of incidence. Let's consider specifically φ=−90° (the case for φ=+90° is essentially identical). No solution for γ exists for the case of m=−1. If m=0 then γ=−90° corresponding to a diffracted beam with a k-vector in the same direction as the incident beam. In the case of m=1, there is a solution for γ provided that λ≦2d. For the typical moth-eye grating period of 250 nm, 2d=500 nm, and visible light with wavelengths smaller than this may be diffracted by the grating. That is why moth-eye surfaces have a characteristic blue-green tint when illuminated and viewed from oblique angles. Interestingly, none of the diffracted beams have a vector component in the same direction as the k-vector of the incident beam. That is, the m=−1 order tends to be diffracted back towards the source, with the color of the diffracted beam going from greenish to more blue as the viewing angle decreases towards the normal.
Two Dimensional Gratings
A real moth-eye surface fabricated by interference lithography is a two-dimensional grating, rather than a one-dimensional grating used in the example above. However, the arguments for the appearance of diffracted orders at high angles of incidence are still valid keeping in mind that diffraction into non-zero orders will occur in preferred azimuthal directions that are consistent with the symmetry of the pattern.
In the 2D case, we can estimate diffraction intensity by numerically summing the phases due to diffraction off of all the individual vertices of the lattice, instead of using (EQ. 1). Strong diffraction intensities will occur in directions for which the phases combine constructively. For instance, consider the diffraction from a square-lattice (as illustrated schematically in FIG. 1), which is usually the pattern used for moth-eye surfaces. If light impinges on this structure at normal incidence, no light will be diffracted into first-order or higher peaks, just as in the 1D case. In order to see non-zeroth order diffraction, light at oblique incidence must be used. FIG. 2 shows the polar distribution (θ, γ) of intensity of diffracted light from a square lattice grating at the oblique angle of illumination σ=0° and φ=60°. Here σ and φ are the polar and azimuthal angles, respectively, in spherical polar coordinates for the incident light, while θ and γ are the corresponding angles for diffracted light. For this calculation, the square lattice grating is oriented so that one of its high symmetry axes is lined up along the σ=0° direction, and its lattice constant has been set to 250 nm. The zeroth order diffraction beam 12 in FIG. 2 has its peak at θ0=180° and γ0=60°. The backscattered m=−1 diffraction beam 14 peaks at θ−1=0° and γ−1≈48°.
The zeroth-order peak makes an angle relative to the normal that is equal to the angle (relative to normal) of the incident beam. Zeroth-order diffraction is what we usually think of as the simple reflection of incident light. For this reason, if we refer to “diffraction” we usually do not mean to include the zeroth-order beam (which from now on will be called the “reflected beam”, and if we wish to “reduce diffraction” what we mean is to reduce first-order or higher diffraction. In this example of the square lattice, the peak intensity of the backscattered diffraction beam 14 is comparable in magnitude to the intensity of the reflected beam 12. The calculation was performed for a finite array of 8×8 lattice sites, and therefore is only an approximation of a truly infinite periodic array, but it does capture fairly quantitatively the optical behavior of the system. We have performed the same calculation for a regular hexagonal lattice (not shown) and found that in this case also, the reflected and backscattered beams are comparable in magnitude.
Also note that these plots use arbitrary units, and although the reflected beam appears prominently, it is actually much smaller compared to the reflected beam in the absence of a textured surface.
A Theoretically Obvious Solution
How can we reduce the intensity of the backscattered diffraction peak? We turn again to (EQ. 1). Recall that the diffraction is possible (for oblique angles of incidence) only if λ≦2d. Therefore if we are able to make d<λ/2, it should be possible to suppress all diffraction (we're not counting the reflected beam as a “diffracted beam”). Thus for the visible waveband, the theoretically obvious solution is simply to fabricate moth-eye on a square lattice where the pitch or lattice constant d (the 2D equivalent of the 1D period d) is smaller than 200 nm. This solution has a tradeoff. The moth-eye protuberances must be relatively tall in order for them to be effective for the long wavelength end of the spectrum. That is, the shorter the protuberances, the less effective the texture is at reducing reflectance, especially for redder light. But if the pitch is decreased, then the aspect ratio between height and pitch must be increased in order to hold the height constant. In terms of microstructure fabrication, it is true that smaller aspect ratios are preferred for reproducibility, ease of replication, and mechanical strength. Therefore, we seek another (not obvious) solution to reduce diffraction without decreasing the overall pitch size or increasing the aspect ratio.
Recap of the Problem
The motheye patterns having nice antireflective properties still demonstrate significant diffraction of light in lower wavelength range for which they were designed. Square and hexagonal lattices produce diffraction patterns that can be visible to the human eye. That makes periodic motheye patterns less effective at high angles of incident and reflected lights. In other words motheye ability to not reflect the light interferes with diffraction effects from incident light leading to backscattering and reflection.